Instead the story is that the source engine was located in the "Src" directory in their Visual Source Safe. And the Half Life 1 engine was in a separate branch named GoldSrc because it was about to ship real soon, and they needed to keep changes to a minimum.
You make me feel old for realising people younger than me have not ever realised this. But it makes sense now I type it... out loud(?)
Back in my day the Steam UI was army green and you'd use it to play all the LAN games your mate had by copying their entire Steam folder over to yours a couple hours before the LAN started. And that was it. That was the "install". You had Steam and all the HL mods like DoD and CS. Primed and ready to get noise complaints from the neighbours.
That's not why it's called that. The real reason is that they didn't bother ever giving it a name. When they needed a stable fork so they could further develop the engine without interfering with the development of Half-Life, they referred to the two source codes "GoldSrc" and "Src" and the name stuck.